The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  1  1  1  1  X  X
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2  0 3X 3X+2  2 3X+2  0
 0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+44x^16+32x^17+204x^18+576x^19+398x^20+480x^21+208x^22+64x^23+34x^24+4x^26+2x^28+1x^32

The gray image is a code over GF(2) with n=160, k=11 and d=64.
This code was found by Heurico 1.16 in 0.015 seconds.